{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5944cad8-2460-4b51-81fb-171f2f9067de",
   "metadata": {},
   "source": [
    "# 数值计算-基于numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1de4ec7c-b311-482b-a1ea-af3da4b06593",
   "metadata": {},
   "source": [
    "# 背景介绍\n",
    "我们使用python作为信息分析的语言在于其简单，易学，但更为重要的是，其对数学计算的友好与便利，其中numpy是python中重要的计算矩阵，向量的工具。其几乎可以认为是python数据科学的核心。因此，我们将对本章内容左宗"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0351f03-8dd0-460c-9612-8ce5dbefa5dc",
   "metadata": {},
   "source": [
    "# Numpy介绍\n",
    "\n",
    "Numpy是python数组计算，矩阵计算和科学计算的核心库。其提供了一个高性能的数组对象，让我们能够轻松地创建多维度数组，并提供了大量的函数和方法，从而广泛地应用在数据分析、机器学习、深度学习等领域中。\n",
    "\n",
    "---\n",
    "在介绍Numpy同时，我们还会介绍如何结合Numpy进行向量计算，线性代数计算等基本知识，以为后期的进一步分析打下基础。\n",
    "\n",
    "本节包含以下内容：\n",
    "\n",
    "1. Numpy 数组创建与操作\n",
    "2. Numpy 中计算方法\n",
    "3. Numpy 线性代数实现"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "715fffe8-97a7-46a6-84c3-019a89310f8c",
   "metadata": {},
   "source": [
    "## Numpy 数组创建与操作\n",
    "1. Numpy 中定义数组\n",
    "\n",
    "\n",
    "```python\n",
    "arr=np.arrary([num1,num2,num3],dytpe=数据类型,ndmin=维度,order)\n",
    "```\n",
    "---\n",
    "2. 指定维度填充数组\n",
    "  * 创建0值数组 \n",
    " ```python \n",
    "  np.zero((shape),dtype)\n",
    "  ```\n",
    "  np.full((shape),填充数值)\n",
    "3. 从数值范围创建数组\n",
    "  * arange 指定步长数组\n",
    "  ```python\n",
    "  arange(start,end,step,dtype)\n",
    "  ```\n",
    "  参数：\n",
    "    *   start:起始值\n",
    "    *   end：终止值\n",
    "    *   step:步长\n",
    "    *   dtype：数值值数据类型\n",
    "  * linspace 等差数组\n",
    "  ```python\n",
    "  linspace(start,end,num,endpoint,retstep,dtype)\n",
    "  ```\n",
    "    参数：\n",
    "    *   start:起始值\n",
    "    *   end：终止值\n",
    "    * num：要生成的等步长数量，默认为50\n",
    "    *   endpoint：如果为True，数列中包含stop参数值\n",
    "    *  retstep：若为True，生成的数组中会显示间距\n",
    "    *   dtype：数值值数据类型\n",
    "  * lospace 等比数组\n",
    "  ```python\n",
    "  logspace(start,end,num,endpoint,base,dtype)\n",
    "  ``   \n",
    "  参数：\n",
    "    *   start:起始值\n",
    "    *   end：终止值\n",
    "    * num：要生成的等步长数量，默认为50\n",
    "    *   endpoint：如果为True，数列中包含stop参数值\n",
    "    *  base:对数log的底数\n",
    "    *   dtype：数值值数据类型`\n",
    "  \n",
    "4. 随机数组\n",
    "随机数组的生成主要使用Numpy中的random模块。\n",
    " \n",
    ">如果希望生成的随机数一致，则使用np.random.seed()\t\n",
    "确定随机数生成的种子，让生成随机数的过程可重现（不设置seed时，每次生成的随机数将不同）\n",
    "   * 0-1范围随机数组\n",
    "   ```python\n",
    "   numpy.random.rand(维度1，维度2...)\n",
    "   ```\n",
    "   ---\n",
    "   * randn从正态分布中返回随机生成的数组\n",
    "   ---\n",
    "   * randint 生成一定范围内的随机整数组，为左闭右开区间\n",
    "   \n",
    "   ```python\n",
    "   numpy.random.randint(low,high,size)\n",
    "   ```\n",
    "      参数：\n",
    "   * low:起始低值\n",
    "   * high：终止值\n",
    "   * szie：数组维度\n",
    "   ---\n",
    "   * normal 生成正态分布的数组\n",
    "   \n",
    "   ```python \n",
    " \n",
    "   numpy.random.normal(loc,scale,size)\n",
    "   ```\n",
    "   \n",
    "   参数：\n",
    "   * loc:正态分布的均值，位于分布中心\n",
    "   * scale:正态分布的标准差\n",
    "   * szie：数组维度\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "95d5b506-8783-4925-b075-fe76b03880f2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-03-17T02:07:19.538394Z",
     "iopub.status.busy": "2022-03-17T02:07:19.537825Z",
     "iopub.status.idle": "2022-03-17T02:07:19.548045Z",
     "shell.execute_reply": "2022-03-17T02:07:19.547392Z",
     "shell.execute_reply.started": "2022-03-17T02:07:19.538357Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2-2全1数组： \n",
      " [[1 1]\n",
      " [1 1]]\n",
      "3-3全0数组： \n",
      " [[0 0 0]\n",
      " [0 0 0]\n",
      " [0 0 0]]\n",
      "指定数值3-3数组： \n",
      " [[3.14 3.14 3.14]\n",
      " [3.14 3.14 3.14]\n",
      " [3.14 3.14 3.14]]\n",
      "5-5特征矩阵 \n",
      " [[1. 0. 0. 0. 0.]\n",
      " [0. 1. 0. 0. 0.]\n",
      " [0. 0. 1. 0. 0.]\n",
      " [0. 0. 0. 1. 0.]\n",
      " [0. 0. 0. 0. 1.]]\n",
      "生成3-3空数组, \n",
      " [[3.14 3.14 3.14]\n",
      " [3.14 3.14 3.14]\n",
      " [3.14 3.14 3.14]]\n"
     ]
    }
   ],
   "source": [
    "#生成数组\n",
    "import numpy as np \n",
    "ar1=np.ones((2,2),dtype=int)\n",
    "print(\"2-2全1数组：\",'\\n',ar1)\n",
    "ar2=np.zeros((3,3),dtype=int)\n",
    "print(\"3-3全0数组：\",'\\n',ar2)\n",
    "ar3=np.full((3,3),3.14)\n",
    "print(\"指定数值3-3数组：\",'\\n',ar3)\n",
    "ar4=np.eye(5,dtype=float)\n",
    "print(\"5-5特征矩阵\",'\\n',ar4)\n",
    "ar5=np.empty((3,3))\n",
    "print(\"生成3-3空数组,\",'\\n',ar5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "b384a02a-c496-431a-9888-94cbd7817405",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-03-16T03:23:40.369227Z",
     "iopub.status.busy": "2022-03-16T03:23:40.368697Z",
     "iopub.status.idle": "2022-03-16T03:23:40.506442Z",
     "shell.execute_reply": "2022-03-16T03:23:40.505866Z",
     "shell.execute_reply.started": "2022-03-16T03:23:40.369194Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24\n",
      " 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48\n",
      " 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72\n",
      " 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96\n",
      " 97 98 99]\n",
      "[  1.   2.   3.   4.   5.   6.   7.   8.   9.  10.  11.  12.  13.  14.\n",
      "  15.  16.  17.  18.  19.  20.  21.  22.  23.  24.  25.  26.  27.  28.\n",
      "  29.  30.  31.  32.  33.  34.  35.  36.  37.  38.  39.  40.  41.  42.\n",
      "  43.  44.  45.  46.  47.  48.  49.  50.  51.  52.  53.  54.  55.  56.\n",
      "  57.  58.  59.  60.  61.  62.  63.  64.  65.  66.  67.  68.  69.  70.\n",
      "  71.  72.  73.  74.  75.  76.  77.  78.  79.  80.  81.  82.  83.  84.\n",
      "  85.  86.  87.  88.  89.  90.  91.  92.  93.  94.  95.  96.  97.  98.\n",
      "  99. 100.]\n",
      "[                  1                   2                   4\n",
      "                   8                  16                  32\n",
      "                  64                 128                 256\n",
      "                 512                1024                2048\n",
      "                4096                8192               16384\n",
      "               32768               65536              131072\n",
      "              262144              524288             1048576\n",
      "             2097152             4194304             8388608\n",
      "            16777216            33554432            67108864\n",
      "           134217728           268435456           536870912\n",
      "          1073741824          2147483648          4294967296\n",
      "          8589934592         17179869184         34359738368\n",
      "         68719476736        137438953472        274877906944\n",
      "        549755813888       1099511627776       2199023255552\n",
      "       4398046511104       8796093022208      17592186044416\n",
      "      35184372088832      70368744177664     140737488355328\n",
      "     281474976710656     562949953421312    1125899906842624\n",
      "    2251799813685248    4503599627370496    9007199254740992\n",
      "   18014398509481984   36028797018963968   72057594037927936\n",
      "  144115188075855872  288230376151711744  576460752303423488\n",
      " 1152921504606846976 2305843009213693952 4611686018427387904\n",
      " 9223372036854775808]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#从数值范围创建数组\n",
    "import numpy as np \n",
    "a1=np.arange(1,100,1)# 注意arange是左闭右开区间[start,end)\n",
    "print(a1)\n",
    "a2=np.linspace(1,100,100)#注意linspace是左闭右闭区间[start,end]\n",
    "print(a2)\n",
    "a3=np.logspace(0,63,64,base=2,dtype='uint64')#注意需要用uint64数据类型，否则会溢出\n",
    "print(a3)\n",
    "import matplotlib.pyplot as plt \n",
    "fig,axes=plt.subplots()\n",
    " \n",
    "axes.plot(a3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "0ba71cdc-4298-47bc-9d54-f31f86e91e5a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-03-16T04:01:11.066214Z",
     "iopub.status.busy": "2022-03-16T04:01:11.065607Z",
     "iopub.status.idle": "2022-03-16T04:01:11.576637Z",
     "shell.execute_reply": "2022-03-16T04:01:11.575951Z",
     "shell.execute_reply.started": "2022-03-16T04:01:11.066181Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "生成二维随机数组： [[0.53390175 0.26850328]\n",
      " [0.85539098 0.93217819]\n",
      " [0.63377018 0.8952355 ]\n",
      " [0.92529424 0.64890462]\n",
      " [0.1270419  0.88446983]]\n",
      "[-1.77545287  0.19977893 -2.27006845  0.02105901  0.56397463  0.18544028\n",
      " -0.32671559  1.92598904 -0.38700658  0.54165922 -0.18552803  0.29866612\n",
      "  1.50490949 -1.14079203 -0.85304726 -0.21998762 -0.09807932  0.34752619\n",
      "  0.51764724 -1.05126854 -0.81763971 -1.41776939  0.98095273  1.03564273\n",
      " -1.90740747  0.64030045  0.70991474 -0.00238994  1.11355571 -1.50309958\n",
      "  1.57691032 -0.17667858  0.61913841 -2.26018999 -2.03230462 -0.40984544\n",
      "  0.4284987   0.65217971  1.36851165 -0.65315368  2.21717324  2.01550535\n",
      " -0.06305303 -0.84860812 -0.10243971  0.39378668  0.65899166  0.74837016\n",
      " -1.07585753 -0.76040787 -0.41445911 -0.87829541 -1.77727991  0.46180324\n",
      " -0.921349    0.26763     1.20749231  0.29356179  0.22080037  0.68187582\n",
      "  0.88366725 -0.06060048 -0.13972353  1.00558001  0.52462103  0.24569836\n",
      " -0.91551732  0.41142808 -1.25759095 -0.10853764 -1.21455752  2.18861102\n",
      "  0.9529367  -0.40816226 -0.56808992  0.27122561 -0.46292391 -1.34790412\n",
      "  0.15240155  0.13768755  0.42383242 -0.00321102 -0.83967835 -0.78453227\n",
      "  1.58777328 -0.66485468  0.72178537 -0.23005371  0.13994756  0.74740733\n",
      "  0.43383637  0.21789719 -0.58673972  0.33180082 -0.81862329 -0.4809976\n",
      "  1.39601519  1.12387864 -0.08557274 -0.69586531]\n",
      "生成1-10（不包括10）的10个随机整数： [96 63 69 42 99 72 41 75 59 44 92 41 45 22 37 38 88 60 57 23 21 95 99 41\n",
      "  3 79 15 48 10 44 48 44 63 74 69 65 91 41 88 76 16 41 14 11 70 91 52 81\n",
      " 74 52 56 55 48 93 17 92 48 70 15 11 90 36 50 26 91 20 33 11 40  3 42 90\n",
      " 70 76 38 10 26 79 65 21 52 27 47 34 11 43 33 77 42 92 73 41 60 85 74 50\n",
      " 49 60 89 90]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f6b1576ea50>]"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 随机数组\n",
    "import numpy as np \n",
    "n=np.random.rand(5,2)\n",
    "print(\"生成二维随机数组：\",n)\n",
    "n1=np.random.randn(100)\n",
    "print(n1)\n",
    "import matplotlib.pyplot as plt \n",
    "fig,axes=plt.subplots(2,2)\n",
    "ax1=axes[0,0]\n",
    "ax1.hist(n1)\n",
    "ax1.grid()\n",
    "n2=np.random.randint(1,100,100)\n",
    "print(\"生成1-10（不包括10）的10个随机整数：\",n2)\n",
    "n3=np.random.normal(0,10,1000)\n",
    "ax2=axes[0,1]\n",
    "ax2.hist(n3)\n",
    "ax2.grid()\n",
    "ax3=axes[1,0]\n",
    "ax3.plot(n2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcb63e75-0daa-4c20-9f45-e4b9f6de23b6",
   "metadata": {},
   "source": [
    "### 数组的属性\n",
    "Numpy中，每个数组都有ndim（数组的维度），shape（数组每个维度的大小），size（数组总的大小）等属性。\n",
    "* ndarray.ndim\n",
    "\n",
    "the number of axes (dimensions) of the array.\n",
    "\n",
    "* ndarray.shape\n",
    "\n",
    "the dimensions of the array. This is a tuple of integers indicating the size of the array in each dimension. For a matrix with n rows and m columns, shape will be (n,m). The length of the shape tuple is therefore the number of axes, ndim.\n",
    "\n",
    "* ndarray.size\n",
    "\n",
    "the total number of elements of the array. This is equal to the product of the elements of shape.\n",
    "\n",
    "* ndarray.dtype\n",
    "\n",
    "an object describing the type of the elements in the array. One can create or specify dtype’s using standard Python types. Additionally NumPy provides types of its own. numpy.int32, numpy.int16, and numpy.float64 are some examples.\n",
    "\n",
    "* ndarray.itemsize\n",
    "\n",
    "the size in bytes of each element of the array. For example, an array of elements of type float64 has itemsize 8 (=64/8), while one of type complex32 has itemsize 4 (=32/8). It is equivalent to ndarray.dtype.itemsize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9d720a42-eeb0-45a7-bfac-c7e2e9f3817c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-03-15T01:36:00.204502Z",
     "iopub.status.busy": "2022-03-15T01:36:00.204085Z",
     "iopub.status.idle": "2022-03-15T01:36:00.212071Z",
     "shell.execute_reply": "2022-03-15T01:36:00.211390Z",
     "shell.execute_reply.started": "2022-03-15T01:36:00.204468Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15]]\n",
      "数组的维度:  2\n",
      "数组的形状： (1, 15)\n",
      "数组中元素个数： 15\n",
      "数组中数据类型： int64\n"
     ]
    }
   ],
   "source": [
    "# 数组的属性\n",
    "import numpy as np \n",
    "arr1=np.array([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],ndmin=2)\n",
    "#arr1=np.arange(15).reshape(3,5)\n",
    "print(arr1)\n",
    "print(\"数组的维度: \",arr1.ndim)\n",
    " \n",
    "print(\"数组的形状：\",arr1.shape)\n",
    "print(\"数组中元素个数：\",arr1.size)\n",
    "print(\"数组中数据类型：\",arr1.dtype.name)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fc9a8cc-2902-40b8-ac34-8a6d28066d1b",
   "metadata": {},
   "source": [
    "### 数组的索引（获取数值）\n",
    "与list一样，数组中索引index也是从0开始，由[]进行指定返回。\n",
    "```python\n",
    "array[index,index]=newValue\n",
    "```\n",
    "### 数组的切片（获取子数组）\n",
    "可以通过切片（slice）获取子数组，为了获取数组x的一个切片，可以使用如下代码：\n",
    "```python\n",
    "x[start:stop:step]\n",
    "```\n",
    "其中start为开始索引，stop为结束，step为取值步长\n",
    "\n",
    "> 注意：Numpy中数组的切片返回的是原始数组的视图（view)而非如list切片返回的是原始list的副本，这意味对数组切片的修改将修改原始数据。如果希望不修改原始数组，则可以使用.copy()方法。\n",
    "\n",
    "###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "e32e3e71-a68c-4aa3-b99f-47337608062c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-03-15T02:29:42.779204Z",
     "iopub.status.busy": "2022-03-15T02:29:42.778775Z",
     "iopub.status.idle": "2022-03-15T02:29:42.788517Z",
     "shell.execute_reply": "2022-03-15T02:29:42.787883Z",
     "shell.execute_reply.started": "2022-03-15T02:29:42.779172Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14]\n",
      "获取第三个数组元素： 2\n",
      "修改指定元素值: [ 0  1 19  3  4  5  6  7  8  9 10 11 12 13 14]\n",
      "对数组进行切片,间隔一个元素： [19  4  6  8]\n",
      "逆序取值 [14 13 12 11 10  9  8  7  6  5  4  3 19  1  0]\n",
      "[[ 0  1  2  3  4]\n",
      " [ 5  6  7  8  9]\n",
      " [10 11 12 13 14]\n",
      " [15 16 17 18 19]]\n",
      "选取第二行，第三列的元素 13\n",
      "选取二行，三列的切片 [[0 1 2]\n",
      " [5 6 7]]\n",
      "选取单行： [10 11 12 13 14]\n",
      "选取单列： [ 1  6 11 16]\n"
     ]
    }
   ],
   "source": [
    "# 一维向量的操作\n",
    "import numpy as np \n",
    "arr2=np.arange(15)\n",
    "print(arr2)\n",
    "print(\"获取第三个数组元素：\", arr2[2])\n",
    "arr2[2]=19\n",
    "print(\"修改指定元素值:\",arr2)\n",
    "arr2[2:5]\n",
    "print(\"对数组进行切片,间隔一个元素：\",arr2[2:10:2])\n",
    "print(\"逆序取值\", arr2[::-1])\n",
    "### 二维数组切片操作\n",
    "arr3=np.arange(20).reshape(4,5)\n",
    "print(arr3)\n",
    "print(\"选取第二行，第三列的元素\",arr3[2,3])\n",
    "print(\"选取二行，三列的切片\",arr3[:2,:3])\n",
    "print(\"选取单行：\",arr3[2,:])\n",
    "print(\"选取单列：\",arr3[:,1])\n"
   ]
  },
  {
   "cell_type": "code",
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   "id": "36e3a014-caef-40b9-abf2-2febe9c975b3",
   "metadata": {
    "execution": {
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    },
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "修改前子数组： [[21  1]\n",
      " [ 5  6]]\n",
      "修改后子数组： [[21  1]\n",
      " [ 5  6]]\n",
      "修改后的母数组： [[21  1  2  3  4]\n",
      " [ 5  6  7  8  9]\n",
      " [10 11 12 13 14]\n",
      " [15 16 17 18 19]]\n",
      "[100, 2]\n",
      "[1, 2, 3, 4, 5]\n",
      "新的子数组副本： [[21  1]\n",
      " [ 5  6]]\n",
      "子数组修改后值： [[21  1]\n",
      " [ 5 22]]\n",
      "原始数组没有受到影响 [[21  1  2  3  4]\n",
      " [ 5  6  7  8  9]\n",
      " [10 11 12 13 14]\n",
      " [15 16 17 18 19]]\n"
     ]
    }
   ],
   "source": [
    "# 子数组的修改将会影响到原始母数组\n",
    "arr3_1=arr3[:2,:2]\n",
    "print(\"修改前子数组：\",arr3_1)\n",
    "arr3_1[0,0]=21\n",
    "print(\"修改后子数组：\",arr3_1)\n",
    "print(\"修改后的母数组：\",arr3)\n",
    "# 对比list\n",
    "list1=[1,2,3,4,5]\n",
    "list1_1=list1[0:2]\n",
    "list1_1[0]=100\n",
    "print(list1_1)\n",
    "print(list1)\n",
    "# 使用copy方法创建数组副本，从而不修改原始数组\n",
    "arr3_2=arr3[:2,:2].copy()\n",
    "print(\"新的子数组副本：\",arr3_2)\n",
    "arr3_2[1,1]=22\n",
    "print(\"子数组修改后值：\",arr3_2)\n",
    "print(\"原始数组没有受到影响\",arr3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88274191-2af8-4fa8-8f45-16fd038e3748",
   "metadata": {},
   "source": [
    "### 数组的变形\n",
    "1. reshape进行数组变形\n",
    "\n",
    "Numpy中，可以使用reshape（行，列）来对数组形状进行变形。\n",
    "此外，可以使用np.newaxis关键字，将一维数组转换为二维的行、列矩阵\n",
    "\n",
    "2. 数组的转置\n",
    "\n",
    "转置是一种特殊的数据重组形式，可以返回底层数据的视图而不需要复制任何内容，Numpy中转置方法为\n",
    "```python\n",
    "arr.transpose((新维度，新维度，新维度))\n",
    "#或者\n",
    "arr.T\n",
    "```\n",
    "\n",
    "3. 将多维数组变为一维数组 \n",
    "```python\n",
    "numpy.flatten()\n",
    "```\n",
    "---\n",
    "### 数组拼接分裂\n",
    "1. 数组的拼接\n",
    "在Numpy中数组的拼接主要通过以下方法实现：\n",
    "\n",
    "```python\n",
    "np.concatenate([arr1,arr2,...],axis=ndim)# axis为拼接的维度\n",
    "np.vstack(arr1,arr2,...)# 垂直拼接\n",
    "np.hstack(arr1,arr2,...)# 水平拼接\n",
    "```\n",
    "---\n",
    "2. 数组的分裂\n",
    "与拼接相反，数组可以通过np.split,np.hsplit,np.vsplit实现分裂。np.split()函数的作用是将一个数组拆分为多个子数组 \n",
    "```python\n",
    "np.splict(ary,indices_or_sections,axis,res)\n",
    "```\n",
    "* ary\n",
    "\n",
    " ary的类型为ndarray（n维数组），表示待分割的原始数组\n",
    "* indices_or_sections\n",
    "\n",
    " indices_or_sections的类型为int或者一维数组，表示一个索引，也就是切的位置所在。indices_or_sections的值如果是一个整数的话，就用这个数平均分割原数组。indices_or_sections的值如果是一个数组的话，就以数组中的数字为索引切开，这个不是太好理解，待会看例子应该就容易理解了。\n",
    "* axis\n",
    "\n",
    " axis的类型为int，表示的是沿哪个维度切。ary为2维数组时，axis默认为0表示横向切，为1时表示纵向切。\n",
    "* res\n",
    "\n",
    " 返回值res的类型为ndarray（n维数组），表示返回的是一组字数组。\n",
    " \n",
    " ### 数组删除\n",
    " Numpy中对数组某部分数据的删除主要用delete方法\n",
    " ```python\n",
    " np.delete(array,obj,axis)\n",
    " ```\n",
    " 参数：\n",
    " \n",
    "*  array:需要处理的矩阵\n",
    "\n",
    "* obj:需要处理的位置，比如要删除的第一行或者第一行和第二行\n",
    "\n",
    "* axis:\n",
    "\n",
    "如果输入为None：array会先按行展开，然后按照obj，删除第obj-1(从0开始)位置的数，返回一个行矩阵。\n",
    "\n",
    "如果输入为0：按行删除\n",
    "\n",
    "如果输入为1：按列删除\n",
    " \n",
    " \n",
    " "
   ]
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "转置前数据: \n",
      " [[0.19151945 0.62210877 0.43772774 0.78535858 0.77997581]\n",
      " [0.27259261 0.27646426 0.80187218 0.95813935 0.87593263]\n",
      " [0.35781727 0.50099513 0.68346294 0.71270203 0.37025075]]\n",
      "转置后数据： \n",
      " [[0.19151945 0.27259261 0.35781727]\n",
      " [0.62210877 0.27646426 0.50099513]\n",
      " [0.43772774 0.80187218 0.68346294]\n",
      " [0.78535858 0.95813935 0.71270203]\n",
      " [0.77997581 0.87593263 0.37025075]]\n",
      "变形为2*10的矩阵 [[ 0  1  2  3  4  5  6  7  8  9]\n",
      " [10 11 12 13 14 15 16 17 18 19]]\n",
      "变形为4*5的矩阵 [[ 0  1  2  3  4]\n",
      " [ 5  6  7  8  9]\n",
      " [10 11 12 13 14]\n",
      " [15 16 17 18 19]]\n",
      "转换为二维列矩阵： [[ 0]\n",
      " [ 1]\n",
      " [ 2]\n",
      " [ 3]\n",
      " [ 4]\n",
      " [ 5]\n",
      " [ 6]\n",
      " [ 7]\n",
      " [ 8]\n",
      " [ 9]\n",
      " [10]\n",
      " [11]\n",
      " [12]\n",
      " [13]\n",
      " [14]\n",
      " [15]\n",
      " [16]\n",
      " [17]\n",
      " [18]\n",
      " [19]]\n",
      "转换为二维行矩阵： [[ 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19]]\n",
      "[20 21 22 23 24]\n",
      "axis=0进行拼接 [ 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\n",
      " 24]\n",
      "[[ 0  1  2  3  4]\n",
      " [ 5  6  7  8  9]\n",
      " [10 11 12 13 14]\n",
      " [15 16 17 18 19]]\n",
      "[[20 21 22 23 24]]\n",
      "矩阵行拼接，axis=0 [[ 0  1  2  3  4]\n",
      " [ 5  6  7  8  9]\n",
      " [10 11 12 13 14]\n",
      " [15 16 17 18 19]\n",
      " [20 21 22 23 24]]\n",
      "[[0]\n",
      " [1]\n",
      " [2]\n",
      " [3]]\n",
      "矩阵列拼接,axis=1： [[ 0  1  2  3  4  0]\n",
      " [ 5  6  7  8  9  1]\n",
      " [10 11 12 13 14  2]\n",
      " [15 16 17 18 19  3]]\n",
      "通过vstack进行垂直拼接 [[ 0  1  2  3  4]\n",
      " [ 5  6  7  8  9]\n",
      " [10 11 12 13 14]\n",
      " [15 16 17 18 19]\n",
      " [20 21 22 23 24]]\n",
      "通过hstack进行垂直拼接 [[ 0  1  2  3 20]\n",
      " [ 4  5  6  7 21]\n",
      " [ 8  9 10 11 22]\n",
      " [12 13 14 15 23]\n",
      " [16 17 18 19 24]]\n"
     ]
    }
   ],
   "source": [
    "#数组转置\n",
    "np.random.seed(1234)\n",
    "ar1=np.random.rand(3,5)\n",
    "print(\"转置前数据:\",'\\n',ar1)\n",
    "ar2=ar1.T\n",
    "print(\"转置后数据：\",'\\n',ar2)\n",
    "# 数组的拼接\n",
    "import numpy as np\n",
    "arr=np.arange(20)\n",
    "print(\"变形为2*10的矩阵\",arr.reshape(2,10))\n",
    "print(\"变形为4*5的矩阵\",arr.reshape(4,5))\n",
    "print(\"转换为二维列矩阵：\",arr[:,np.newaxis])\n",
    "print(\"转换为二维行矩阵：\",arr[np.newaxis,:])\n",
    "# 数组的拼接\n",
    "arr1=np.arange(20,25)\n",
    "print(arr1)\n",
    "arr2=np.concatenate([arr,arr1],axis=0)\n",
    "print(\"axis=0进行拼接\",arr2)\n",
    "# 矩阵的拼接\n",
    "arr2=arr.reshape(4,5)\n",
    "arr1_1=arr1[np.newaxis,:]#转换为行向量\n",
    "print(arr2)\n",
    "print(arr1_1)\n",
    "print(\"矩阵行拼接，axis=0\",np.concatenate([arr2,arr1_1],axis=0))\n",
    "arr1_2=np.array([0,1,2,3])\n",
    "arr1_2=arr1_2[:,np.newaxis]# 转换为列向量\n",
    "print(arr1_2)\n",
    "print(\"矩阵列拼接,axis=1：\",np.concatenate([arr2,arr1_2],axis=1))\n",
    "# 通过hstack与vstack实现行列拼接\n",
    "print(\"通过vstack进行垂直拼接\",np.vstack([arr.reshape(4,5),arr1[np.newaxis,:]]))\n",
    "print(\"通过hstack进行垂直拼接\",np.hstack([arr.reshape(5,4),arr1[:,np.newaxis]]))"
   ]
  },
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "带分割矩阵： [[ 0  1  2  3  4  5]\n",
      " [ 6  7  8  9 10 11]\n",
      " [12 13 14 15 16 17]\n",
      " [18 19 20 21 22 23]\n",
      " [24 25 26 27 28 29]]\n",
      "###################\n",
      "[[ 0  1]\n",
      " [ 6  7]\n",
      " [12 13]\n",
      " [18 19]\n",
      " [24 25]]\n",
      "###################\n",
      "[[ 2]\n",
      " [ 8]\n",
      " [14]\n",
      " [20]\n",
      " [26]]\n",
      "###################\n",
      "[[ 3  4  5]\n",
      " [ 9 10 11]\n",
      " [15 16 17]\n",
      " [21 22 23]\n",
      " [27 28 29]]\n",
      "[[[ 0  1  2  3  4]\n",
      "  [ 5  6  7  8  9]]\n",
      "\n",
      " [[10 11 12 13 14]\n",
      "  [15 16 17 18 19]]\n",
      "\n",
      " [[20 21 22 23 24]\n",
      "  [25 26 27 28 29]]]\n",
      "###################\n",
      "[[[ 0  1]\n",
      "  [ 5  6]]\n",
      "\n",
      " [[10 11]\n",
      "  [15 16]]\n",
      "\n",
      " [[20 21]\n",
      "  [25 26]]]\n",
      "###################\n",
      "[[[ 2]\n",
      "  [ 7]]\n",
      "\n",
      " [[12]\n",
      "  [17]]\n",
      "\n",
      " [[22]\n",
      "  [27]]]\n",
      "###################\n",
      "[[[ 3  4]\n",
      "  [ 8  9]]\n",
      "\n",
      " [[13 14]\n",
      "  [18 19]]\n",
      "\n",
      " [[23 24]\n",
      "  [28 29]]]\n",
      "垂直划分vsplit \n",
      "[[ 0  1  2  3  4  5]\n",
      " [ 6  7  8  9 10 11]]\n",
      "###################\n",
      "[[12 13 14 15 16 17]\n",
      " [18 19 20 21 22 23]\n",
      " [24 25 26 27 28 29]]\n",
      "平行划分hsplit\n",
      "[[ 0  1]\n",
      " [ 6  7]\n",
      " [12 13]\n",
      " [18 19]\n",
      " [24 25]]\n",
      "###################\n",
      "[[ 2  3  4  5]\n",
      " [ 8  9 10 11]\n",
      " [14 15 16 17]\n",
      " [20 21 22 23]\n",
      " [26 27 28 29]]\n"
     ]
    }
   ],
   "source": [
    "# 数组的分割\n",
    "import numpy as np \n",
    "arr5=np.arange(30).reshape(5,6)\n",
    "print(\"带分割矩阵：\",arr5)\n",
    "arr5_1,arr5_2,arr5_3=np.split(arr5,[2,3],axis=1)#axis代表分割的维度，0行，1列\n",
    "print(\"###################\")\n",
    "print(arr5_1)\n",
    "print(\"###################\")\n",
    "print(arr5_2)\n",
    "print(\"###################\")\n",
    "print(arr5_3)\n",
    "arr6=np.arange(30).reshape(3,2,5)\n",
    "print(arr6)\n",
    "print(\"###################\")\n",
    "ar1,ar2,ar3=np.split(arr6,[2,3],axis=2)# 三维度数组的划分\n",
    "print(ar1)\n",
    "print(\"###################\")\n",
    "print(ar2)\n",
    "print(\"###################\")\n",
    "print(ar3)\n",
    "#垂直划分vsplit,平行划分hsplit\n",
    "ar1,ar2=np.vsplit(arr5,[2])\n",
    "print(\"垂直划分vsplit \")\n",
    "print(ar1)\n",
    "print(\"###################\")\n",
    "print(ar2)\n",
    "print(\"平行划分hsplit\")\n",
    "ar1,ar2=np.hsplit(arr5,[2])\n",
    "print(ar1)\n",
    "print(\"###################\")\n",
    "print(ar2)"
   ]
  },
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  1  2  3  4  5]\n",
      " [ 6  7  8  9 10 11]\n",
      " [12 13 14 15 16 17]\n",
      " [18 19 20 21 22 23]\n",
      " [24 25 26 27 28 29]]\n",
      "删除后得到新数组： [[ 0  1  2  3  4  5]\n",
      " [ 6  7  8  9 10 11]\n",
      " [18 19 20 21 22 23]\n",
      " [24 25 26 27 28 29]]\n",
      "原始的数组并没有受到影响： [[ 0  1  2  3  4  5]\n",
      " [ 6  7  8  9 10 11]\n",
      " [12 13 14 15 16 17]\n",
      " [18 19 20 21 22 23]\n",
      " [24 25 26 27 28 29]]\n",
      "删除2-3列 [[ 0  3  4  5]\n",
      " [ 6  9 10 11]\n",
      " [12 15 16 17]\n",
      " [18 21 22 23]\n",
      " [24 27 28 29]]\n"
     ]
    }
   ],
   "source": [
    "# 数组删除\n",
    "import numpy as np \n",
    "arr6=np.arange(30).reshape(5,6)\n",
    "print(arr6)\n",
    "# 删除第三行\n",
    "print(\"删除后得到新数组：\",np.delete(arr6,2,axis=0))\n",
    "print(\"原始的数组并没有受到影响：\",arr6)\n",
    "print(\"删除2-3列\",np.delete(arr6,[1,2],axis=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a277072-71d6-4010-a9c4-d04019562a26",
   "metadata": {},
   "source": [
    "### [Numpy 排序](https://www.runoob.com/numpy/numpy-sort-search.html)\n",
    "* numpy.sort()\n",
    "numpy.sort() 函数返回输入数组的排序副本。函数格式如下：\n",
    "``` python\n",
    "numpy.sort(a, axis, kind, order)\n",
    "```\n",
    "参数说明：\n",
    "\n",
    "* a: 要排序的数组\n",
    "* axis: 沿着它排序数组的轴，如果没有数组会被展开，沿着最后的轴排序， axis=0 按列排序，axis=1 按行排序\n",
    "* kind: 默认为'quicksort'（快速排序）\n",
    "* order: 如果数组包含字段，则是要排序的字段\n",
    "* numpy.argsort()\n",
    "numpy.argsort() 函数返回的是数组值从小到大的索引值。"
   ]
  },
  {
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    }
   },
   "cell_type": "markdown",
   "id": "233b2f06-e18e-46da-a61d-71899beb1b02",
   "metadata": {},
   "source": [
    "## Numpy数值计算方法\n",
    "NumPy为python提供了一种快速的面向向量的操作，我们可以简单低对数组执行操作实现数学计算，对数组的操作会被作用于数组中的每一个元素，从而得到更快的效率。\n",
    "\n",
    "NumPy中的向量操作是通过通用函数实现，Numpy通用函数，也可以称为ufunc，是一种在ndarray数据中进行逐个元素操作的函数。某些简单函数接受一个或多个标量数值，并产生一个或多个标量结果，而通用函数就是对这样简单函数的向量化封装，其分为面向一个数组的一元通用函数，和面向两个数组的二元通用函数。\n",
    "1. 一元通用函数\n",
    "\n",
    "\n",
    "| Column 1 | Column 2 | Column 3 |\n",
    "| -------- | -------- | -------- |\n",
    "| Text     | Text     | Text     |\n",
    "\n",
    "\n",
    "![image.png](attachment:8e66ca0b-2f88-4661-b11b-44baef317cb4.png)\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "83fca977-c50e-43d6-99a3-eeff8b9355e3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-03-17T02:38:43.965258Z",
     "iopub.status.busy": "2022-03-17T02:38:43.964843Z",
     "iopub.status.idle": "2022-03-17T02:38:45.181721Z",
     "shell.execute_reply": "2022-03-17T02:38:45.180759Z",
     "shell.execute_reply.started": "2022-03-17T02:38:43.965227Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "分班成绩排序： [[30 34 35 37 38 39 39 41 41 41 42 43 43 45 45 45 46 47 48 48 52 53 55 57\n",
      "  58 58 58 59 60 60 61 63 63 64 66 66 70 74 76 79 80 81 84 84 84 87 92 94\n",
      "  95 99]\n",
      " [30 30 33 36 41 41 42 42 44 45 46 46 47 47 47 48 51 52 52 53 55 57 59 60\n",
      "  61 62 63 67 67 68 70 70 71 72 73 75 78 78 80 80 81 83 87 87 92 92 92 94\n",
      "  96 97]\n",
      " [31 32 33 34 35 36 37 38 39 39 39 43 43 45 48 48 52 55 57 58 58 60 60 60\n",
      "  62 62 63 64 67 69 70 71 72 73 74 74 75 76 78 80 82 82 85 88 92 92 93 95\n",
      "  98 99]]\n",
      "将多维成绩数组变更为一维数组，并排序： [30 30 30 31 32 33 33 34 34 35 35 36 36 37 37 38 38 39 39 39 39 39 41 41\n",
      " 41 41 41 42 42 42 43 43 43 43 44 45 45 45 45 45 46 46 46 47 47 47 47 48\n",
      " 48 48 48 48 51 52 52 52 52 53 53 55 55 55 57 57 57 58 58 58 58 58 59 59\n",
      " 60 60 60 60 60 60 61 61 62 62 62 63 63 63 63 64 64 66 66 67 67 67 68 69\n",
      " 70 70 70 70 71 71 72 72 73 73 74 74 74 75 75 76 76 78 78 78 79 80 80 80\n",
      " 80 81 81 82 82 83 84 84 84 85 87 87 87 88 92 92 92 92 92 92 93 94 94 95\n",
      " 95 96 97 98 99 99]\n",
      "三个班总的成绩平均值为： 61.43333333333333 标准差为： 19.03730256335936 方差为： 362.4188888888889 最高分为： 99 最低分为： 30 中位数为： 60.0\n",
      "三个班总的成绩平均值为(四舍五入）： 61.0 标准差为(向上取整）： 20.0 方差为（向下取整）： 362.0 最高分为： 99 最低分为： 30 中位数为： 60.0\n",
      "每一个班的最高成绩： [99 97 99]\n",
      "每一个班的平均成绩： [59.18 62.8  62.32]\n"
     ]
    }
   ],
   "source": [
    "#一元通用函数计算\n",
    "#虚拟三个班，60个学生的成绩，作为运算对象\n",
    "import numpy as np \n",
    "np.random.seed(10)\n",
    "stu=np.random.randint(30,100,150).reshape(3,50)\n",
    "print(\"分班成绩排序：\",np.sort(stu))\n",
    "stu_all=stu.flatten()\n",
    "print(\"将多维成绩数组变更为一维数组，并排序：\",np.sort(stu_all))\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use(\"ggplot\")\n",
    "fig,axes=plt.subplots(2,2)\n",
    "fig.set_size_inches(12,12)\n",
    "ax1=axes[0,0]\n",
    "ax1.hist(stu_all)\n",
    "ax2=axes[0,1]\n",
    "ax2.boxplot(stu_all)\n",
    "def descStu(arr):\n",
    "    avg=np.mean(arr)\n",
    "    std=np.std(arr)\n",
    "    var=np.var(arr)\n",
    "    max_s=np.max(arr)\n",
    "    min_s=np.min(arr)\n",
    "    med_s=np.median(arr)\n",
    "    return avg,std,var,max_s,min_s,med_s\n",
    "#计算三个班的总成绩平均值，标准差，方差，最高分，最低分，中位数\n",
    "avg_s,std_s,var_s,max_s,min_s,med_s=descStu(stu)\n",
    "\n",
    "print(\"三个班总的成绩平均值为：\",avg_s,\"标准差为：\",std_s,\"方差为：\",var_s,\"最高分为：\",max_s,\"最低分为：\",min_s,\"中位数为：\",med_s)\n",
    "print(\"三个班总的成绩平均值为(四舍五入）：\",np.rint(avg_s),\"标准差为(向上取整）：\",np.ceil(std_s),\"方差为（向下取整）：\",np.floor(var_s),\"最高分为：\",max_s,\"最低分为：\",min_s,\"中位数为：\",med_s)\n",
    "print(\"每一个班的最高成绩：\",stu.max(axis=1))#实现对每一行的数据进行聚合\n",
    "print(\"每一个班的平均成绩：\",stu.mean(axis=1))"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "id": "5993137f-2fc5-47d4-92f5-2388e56dcfe4",
   "metadata": {},
   "source": [
    "2. 二元通用函数\n",
    "一些通用函数，比如add或maximum则会接收两个数组并返回一个数组作为结果，因此称为二元通用函数\n",
    "返回一个数组的二元通用函数举例：\n",
    " \n",
    "![image.png](attachment:b7a7d7cc-40c1-434b-b894-5551bb2bf9c9.png)\n",
    "---\n",
    "**广播：**\n",
    "\n",
    "在Numpy中，广播可以理解为用于不同大小数组的二元通用函数（加减乘除）的规则。\n",
    "\n",
    "* 规则1：如果两个数组的维数不同，那么小维数数组的形状会在最左边补1.\n",
    "* 规则2：如果两个数组的形状在任何一个维度上都不匹配，那么数组的形状会沿着维度为1的维度扩展以匹配另外一个数组的形状\n",
    "* 规则3：如果两个数组的形状在任何一个维度上都不匹配并且没有任何一个维度等于1，那么会引发异常\n",
    "\n",
    ">简单理解：对两个数组，分别比较他们的每一个维度（若其中一个数组没有当前维度则忽略），满足：\n",
    ">* 数组拥有相同形状。\n",
    ">* 当前维度的值相等。\n",
    ">* 当前维度的值有一个是 1。\n",
    ">* 若条件不满足，抛出 \"ValueError: frames are not aligned\" 异常。\n",
    "\n",
    "3. 通过比较逻辑函数进行计算\n",
    "\n",
    "可以使用逻辑函数，实现对数组的逐个元素比较，然后返回满足条件的数组，即使用**掩码**\n",
    "* np.where()\n",
    "\n",
    "Numpy中，首先可以使用where进行逻辑判断其等同于 x if condition else y\n",
    "```python\n",
    "np.wehre(数组条件，结果1，结果2)\n",
    "\n",
    "```\n",
    "* np.any()\n",
    "判断数组中是否有满足条件的元素，有返回True\n",
    "* np.all()\n",
    "判断数组是否所有元素都满足条件，若是返回True\n",
    "* np.count_nonzero()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "bd16be6e-c4a8-45ab-b96f-04551f89c43b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-03-17T02:59:11.796200Z",
     "iopub.status.busy": "2022-03-17T02:59:11.795648Z",
     "iopub.status.idle": "2022-03-17T02:59:11.806838Z",
     "shell.execute_reply": "2022-03-17T02:59:11.805954Z",
     "shell.execute_reply.started": "2022-03-17T02:59:11.796161Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "比较不同班级同一个索引号成绩大小： [30 34 35 37 41 41 42 42 44 45 46 46 47 47 47 48 51 52 52 53 55 57 59 60\n",
      " 61 62 63 67 67 68 70 70 71 72 73 75 78 78 80 80 81 83 87 87 92 92 92 94\n",
      " 96 99]\n",
      "[[1. 1. 1.]\n",
      " [1. 1. 1.]]\n",
      "m数组维度数： 2\n",
      "[0 1 2]\n",
      "a数组维度数： 1\n",
      "ar1 的形状： (2, 2, 3)\n",
      "ar2的形状： (3,)\n",
      "(2, 2, 3)\n",
      "[[[ 0. -1. -2.]\n",
      "  [ 0. -1. -2.]]\n",
      "\n",
      " [[ 0. -1. -2.]\n",
      "  [ 0. -1. -2.]]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "#二元通用函数，在不同数组间进行操作\n",
    "class1=np.sort(stu[0,:])\n",
    "class2=np.sort(stu[1,:])\n",
    "class3=np.sort(stu[2,:])\n",
    "print(\"比较不同班级同一个索引号成绩大小：\",np.maximum(class1,class2,class3))\n",
    "m=np.ones((2,3))\n",
    "print(m)\n",
    "print(\"m数组维度数：\",m.ndim)\n",
    "a=np.arange(3)\n",
    "print(a)\n",
    "print(\"a数组维度数：\",a.ndim)\n",
    "# 广播示例\n",
    "ar1=np.ones([2,2,3])\n",
    "print('ar1 的形状：',ar1.shape)\n",
    " \n",
    "\n",
    "ar2=np.arange(1,4,1)\n",
    "print('ar2的形状：',ar2.shape)\n",
    "ar3=ar1-ar2\n",
    "print(ar3.shape)\n",
    "print(ar3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "198a93fa-1c88-4269-b17e-08a2370171a6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-03-17T03:18:11.962911Z",
     "iopub.status.busy": "2022-03-17T03:18:11.962440Z",
     "iopub.status.idle": "2022-03-17T03:18:11.972760Z",
     "shell.execute_reply": "2022-03-17T03:18:11.972002Z",
     "shell.execute_reply.started": "2022-03-17T03:18:11.962873Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "原始分数： \n",
      " [[60 91 80]\n",
      " [74 92 65]\n",
      " [87 71 88]\n",
      " [73 84 69]\n",
      " [88 34 48]\n",
      " [33 41 75]\n",
      " [78 83 58]\n",
      " [83 64 64]\n",
      " [96 62 59]\n",
      " [35 95 44]]\n",
      "(3,)\n",
      "广播后结果形状： (10, 3)\n",
      "加权乘法结果： \n",
      " [[180 182 400]\n",
      " [222 184 325]\n",
      " [261 142 440]\n",
      " [219 168 345]\n",
      " [264  68 240]\n",
      " [ 99  82 375]\n",
      " [234 166 290]\n",
      " [249 128 320]\n",
      " [288 124 295]\n",
      " [105 190 220]]\n",
      "加权和： \n",
      " [762 731 843 732 572 556 690 697 707 515]\n",
      "加权平均分： \n",
      " [76.2 73.1 84.3 73.2 57.2 55.6 69.  69.7 70.7 51.5]\n"
     ]
    }
   ],
   "source": [
    "# 通过广播机制实现计算加权平均分\n",
    "# 设三门课的学分分别为，3，2，5分\n",
    "score=np.random.randint(30,100,30).reshape(10,3)# 三门课10个人的分数\n",
    "print(\"原始分数：\",'\\n',score)\n",
    "weight=np.array([3,2,5])\n",
    "print(weight.shape)\n",
    "w_s=score*weight# 通过广播实现不同形状数组之间可以相乘\n",
    "print(\"广播后结果形状：\",w_s.shape)\n",
    "print(\"加权乘法结果：\",'\\n',w_s)\n",
    "w_s_sum=np.sum(w_s,axis=1)\n",
    "print(\"加权和：\",'\\n',w_s_sum)\n",
    "print(\"加权平均分：\",'\\n',w_s_sum/np.sum(weight))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "4f4c82e8-346b-44f7-9883-1611f8ae0aaa",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-03-17T03:39:09.467738Z",
     "iopub.status.busy": "2022-03-17T03:39:09.467279Z",
     "iopub.status.idle": "2022-03-17T03:39:09.475489Z",
     "shell.execute_reply": "2022-03-17T03:39:09.474904Z",
     "shell.execute_reply.started": "2022-03-17T03:39:09.467702Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "返回所有大于60的分数： [94 70 66 84 92 63 79 81 84 99 95 61 87 66 76 63 74 80 84 64 92 87 72 87\n",
      " 80 75 70 67 81 80 83 78 62 71 61 94 68 96 97 92 92 78 67 63 73 70 73 92\n",
      " 71 63 69 62 82 98 95 82 78 92 72 64 70 76 62 88 99 75 80 74 93 67 85 74]\n",
      "大于60小于80的人数： 39\n",
      "每个班（每行），大于90分人数： [4 6 6]\n",
      "是否有人低于20分： False\n",
      "是否所有人都及格了: False\n"
     ]
    }
   ],
   "source": [
    "# Numpy 逻辑条件\n",
    "# 通过where 函数，将原始分数转换为“及格”,\"不及格\"形式\n",
    "np.where(stu>60,'及格','不及格')\n",
    "# 通过布尔表达作为掩码\n",
    "print(\"返回所有大于60的分数：\",stu[stu>60])\n",
    "# 统计大于60分小于80分的人数\n",
    "print(\"大于60小于80的人数：\",np.sum((stu>60)&(stu<80)))\n",
    "# 统计每行（每个班），大于90分的人数\n",
    "print(\"每个班（每行），大于90分人数：\",np.sum(stu>90,axis=1))\n",
    "#是否有人低于20分？\n",
    "print(\"是否有人低于20分：\",np.any(stu<20))\n",
    "#是不是所有人都及格了？\n",
    "print(\"是否所有人都及格了:\", np.all(stu>=60))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dead9060-8084-4b24-b3e9-6e436d8c4dc7",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "c4472882-766b-4f16-a4a2-21aefb02c14b",
   "metadata": {},
   "source": [
    "# Numpy 线性代数实现\n",
    "了解了Numpy的基础知识后，我们可以使用Numpy来进行线性代数的计算。以下我们将复习线性代数的一些基本概念，并结合Numpy实现计算机的实现。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73e3e80a-ece4-4ae8-a7d8-298df600e9e2",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b2a7fd4d-ea8d-43cd-9590-8d9454898c54",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-03-17T07:26:55.422895Z",
     "iopub.status.busy": "2022-03-17T07:26:55.422236Z",
     "iopub.status.idle": "2022-03-17T07:26:56.399607Z",
     "shell.execute_reply": "2022-03-17T07:26:56.398894Z",
     "shell.execute_reply.started": "2022-03-17T07:26:55.422860Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "7123dc30-dc68-4074-abfe-f49a31d544dc",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d9e0a005-d8ab-4d72-8a43-82643fe6db1c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-03-17T07:28:55.199706Z",
     "iopub.status.busy": "2022-03-17T07:28:55.198941Z",
     "iopub.status.idle": "2022-03-17T07:28:55.204772Z",
     "shell.execute_reply": "2022-03-17T07:28:55.204198Z",
     "shell.execute_reply.started": "2022-03-17T07:28:55.199670Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "向量大小为： 2.23606797749979\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "86a03afc-c4ec-457b-8402-f527e19f3980",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "119cf918-cab0-49c2-b11b-6feb607653d1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-03-17T07:33:59.568641Z",
     "iopub.status.busy": "2022-03-17T07:33:59.568094Z",
     "iopub.status.idle": "2022-03-17T07:33:59.573310Z",
     "shell.execute_reply": "2022-03-17T07:33:59.572646Z",
     "shell.execute_reply.started": "2022-03-17T07:33:59.568570Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.23606797749979\n"
     ]
    }
   ],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "ade33f8a-fbec-46df-8a90-9633c6455c17",
   "metadata": {},
   "source": [
    "### Calculating Direction\n",
    "To calculate the direction, or *amplitude*, of a vector from its cartesian coordinates, you must employ a little trigonometry. We can get the angle of the vector by calculating the *inverse tangent*; sometimes known as the *arctan* (the *tangent*  calculates an angle as a ratio - the inverse tangent, or **tan<sup>-1</sup>**, expresses this in degrees).\n",
    "\n",
    "In any right-angled triangle, the tangent is calculated as the *opposite* over the *adjacent*. In a two dimensional vector, this is the *y* value over the *x* value, so for our **v** vector (2,1):\n",
    "\n",
    "\\begin{equation}tan(\\theta) = \\frac{1}{2}\\end{equation}\n",
    "\n",
    "This produces the result ***0.5***, from which we can use a calculator to calculate the inverse tangent to get the angle in degrees:\n",
    "\n",
    "\\begin{equation}\\theta = tan^{-1} (0.5) \\approx 26.57^{o}\\end{equation}\n",
    "\n",
    "Note that the direction angle is indicated as ***&theta;***.\n",
    "\n",
    "Run the following Python code to confirm this:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e0ccd55-77aa-43b1-861d-1b6f75cce641",
   "metadata": {},
   "source": [
    "### 向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2cd3edb1-ff6b-476b-a69c-338f2696a9e7",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": []
  }
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